On gauge independence in quantum gravity Original Research Article

We prove the gauge independence of the one-loop path integral for on-shell quantum gravity obtained in the framework of the modified geometric approach. We use a projector on pure gauge directions constructed via the quadratic form of the action. This enables us to formulate the proof entirely in terms of determinants of non-degenerate elliptic operators without reference to any renormalization procedure. The role of the rotation of the conformal factor in achieving gauge independence is discussed. Direct computations on CP2 in a general three-parameter background gauge are presented. We comment on the gauge dependence of previous results by Ichinose.